author  wenzelm 
Wed, 06 Aug 1997 15:07:33 +0200  
changeset 3632  17527284f100 
parent 3395  d8700b008944 
child 3764  fe7719aee219 
permissions  rwrr 
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(* Title: Pure/axclass.ML 
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ID: $Id$ 
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Author: Markus Wenzel, TU Muenchen 
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560  5 
User interfaces for axiomatic type classes. 
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*) 
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signature AX_CLASS = 
1498  9 
sig 
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val add_thms_as_axms: (string * thm) list > theory > theory 

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val add_classrel_thms: thm list > theory > theory 

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val add_arity_thms: thm list > theory > theory 

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val add_axclass: class * class list > (string * string) list 

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> theory > theory 

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val add_axclass_i: class * class list > (string * term) list 

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> theory > theory 

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val add_inst_subclass: class * class > string list > thm list 

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> tactic option > theory > theory 

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val add_inst_arity: string * sort list * class list > string list 

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> thm list > tactic option > theory > theory 

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val axclass_tac: theory > thm list > tactic 

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val prove_subclass: theory > class * class > thm list 

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> tactic option > thm 

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val prove_arity: theory > string * sort list * class > thm list 

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> tactic option > thm 

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val goal_subclass: theory > class * class > thm list 

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val goal_arity: theory > string * sort list * class > thm list 

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end; 

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1498  30 
structure AxClass : AX_CLASS = 
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struct 
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(** utilities **) 
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(* type vars *) 
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fun map_typ_frees f (Type (t, tys)) = Type (t, map (map_typ_frees f) tys) 
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 map_typ_frees f (TFree a) = f a 
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 map_typ_frees _ a = a; 
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val map_term_tfrees = map_term_types o map_typ_frees; 
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fun aT S = TFree ("'a", S); 
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3395  45 
fun dest_varT (TFree (x, S)) = ((x, ~1), S) 
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 dest_varT (TVar xi_S) = xi_S 

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 dest_varT T = raise_type "dest_varT" [T] []; 

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(* get axioms and theorems *) 
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fun get_ax thy name = 
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Some (get_axiom thy name) handle THEORY _ => None; 
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val get_axioms = mapfilter o get_ax; 
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val is_def = Logic.is_equals o #prop o rep_thm; 
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fun witnesses thy axms thms = 
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map (get_axiom thy) axms @ thms @ filter is_def (map snd (axioms_of thy)); 
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560  64 
(** abstract syntax operations **) 
423  65 

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(* subclass relations as terms *) 

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1498  68 
fun mk_classrel (c1, c2) = Logic.mk_inclass (aT [c1], c2); 
423  69 

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fun dest_classrel tm = 

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let 

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fun err () = raise_term "dest_classrel" [tm]; 

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3395  74 
val (ty, c2) = Logic.dest_inclass tm handle TERM _ => err (); 
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val c1 = (case dest_varT ty of (_, [c]) => c  _ => err ()) 

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handle TYPE _ => err (); 

423  77 
in 
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(c1, c2) 

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end; 

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81 

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(* arities as terms *) 

83 

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fun mk_arity (t, ss, c) = 

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let 

449  86 
val names = tl (variantlist (replicate (length ss + 1) "'", [])); 
2266  87 
val tfrees = ListPair.map TFree (names, ss); 
423  88 
in 
1498  89 
Logic.mk_inclass (Type (t, tfrees), c) 
423  90 
end; 
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fun dest_arity tm = 

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let 

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fun err () = raise_term "dest_arity" [tm]; 

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3395  96 
val (ty, c) = Logic.dest_inclass tm handle TERM _ => err (); 
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val (t, tvars) = 

423  98 
(case ty of 
3395  99 
Type (t, tys) => (t, map dest_varT tys handle TYPE _ => err ()) 
423  100 
 _ => err ()); 
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val ss = 

3395  102 
if null (gen_duplicates eq_fst tvars) 
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then map snd tvars else err (); 

423  104 
in 
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(t, ss, c) 

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end; 

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560  110 
(** add theorems as axioms **) 
423  111 

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fun prep_thm_axm thy thm = 

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let 

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fun err msg = raise THM ("prep_thm_axm: " ^ msg, 0, [thm]); 

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1237  116 
val {sign, hyps, prop, ...} = rep_thm thm; 
423  117 
in 
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if not (Sign.subsig (sign, sign_of thy)) then 

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err "theorem not of same theory" 

1237  120 
else if not (null (extra_shyps thm)) orelse not (null hyps) then 
423  121 
err "theorem may not contain hypotheses" 
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else prop 

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end; 

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(*general theorems*) 

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fun add_thms_as_axms thms thy = 

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add_axioms_i (map (apsnd (prep_thm_axm thy)) thms) thy; 

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(*theorems expressing class relations*) 

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fun add_classrel_thms thms thy = 

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let 

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fun prep_thm thm = 

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let 

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val prop = prep_thm_axm thy thm; 

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val (c1, c2) = dest_classrel prop handle TERM _ => 

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raise THM ("add_classrel_thms: theorem is not a class relation", 0, [thm]); 

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in (c1, c2) end; 

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in 

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add_classrel (map prep_thm thms) thy 

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end; 

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(*theorems expressing arities*) 

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fun add_arity_thms thms thy = 

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let 

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fun prep_thm thm = 

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let 

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val prop = prep_thm_axm thy thm; 

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val (t, ss, c) = dest_arity prop handle TERM _ => 

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raise THM ("add_arity_thms: theorem is not an arity", 0, [thm]); 

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in (t, ss, [c]) end; 

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in 

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add_arities (map prep_thm thms) thy 

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end; 

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(** add axiomatic type classes **) 

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(* errors *) 
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fun err_not_logic c = 
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error ("Axiomatic class " ^ quote c ^ " not subclass of \"logic\""); 
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fun err_bad_axsort ax c = 
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error ("Sort constraint in axiom " ^ quote ax ^ " not supersort of " ^ quote c); 
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fun err_bad_tfrees ax = 
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error ("More than one type variable in axiom " ^ quote ax); 
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(* ext_axclass *) 
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fun ext_axclass prep_axm (class, super_classes) raw_axioms old_thy = 
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let 
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val axioms = map (prep_axm (sign_of old_thy)) raw_axioms; 
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val thy = add_classes [(class, super_classes)] old_thy; 
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val sign = sign_of thy; 
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(* prepare abstract axioms *) 
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fun abs_axm ax = 
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if null (term_tfrees ax) then 
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Logic.mk_implies (Logic.mk_inclass (aT logicS, class), ax) 
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else 
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map_term_tfrees (K (aT [class])) ax; 
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val abs_axioms = map (apsnd abs_axm) axioms; 
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(* prepare introduction orule *) 
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val _ = 
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if Sign.subsort sign ([class], logicS) then () 
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else err_not_logic class; 
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fun axm_sort (name, ax) = 
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(case term_tfrees ax of 
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[] => [] 
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 [(_, S)] => 
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if Sign.subsort sign ([class], S) then S 
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else err_bad_axsort name class 
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 _ => err_bad_tfrees name); 
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val axS = Sign.norm_sort sign (logicC :: List.concat(map axm_sort axioms)) 
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1498  207 
val int_axm = Logic.close_form o map_term_tfrees (K (aT axS)); 
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fun inclass c = Logic.mk_inclass (aT axS, c); 

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1498  210 
val intro_axm = Logic.list_implies 
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(map inclass super_classes @ map (int_axm o snd) axioms, inclass class); 
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in 
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add_axioms_i ((class ^ "I", intro_axm) :: abs_axioms) thy 
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end; 
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(* external interfaces *) 
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val add_axclass = ext_axclass read_axm; 
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val add_axclass_i = ext_axclass cert_axm; 
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423  224 
(** prove class relations and type arities **) 
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(* class_axms *) 

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fun class_axms thy = 
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let 
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val classes = Sign.classes (sign_of thy); 
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val intros = map (fn c => c ^ "I") classes; 
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in 
1217  233 
map (class_triv thy) classes @ 
234 
get_axioms thy intros 

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end; 
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423  237 

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(* axclass_tac *) 

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(*(1) repeatedly resolve goals of form "OFCLASS(ty, c_class)", 
1217  241 
try class_trivs first, then "cI" axioms 
423  242 
(2) rewrite goals using user supplied definitions 
243 
(3) repeatedly resolve goals with user supplied nondefinitions*) 

244 

245 
fun axclass_tac thy thms = 

1217  246 
let 
247 
val defs = filter is_def thms; 

248 
val non_defs = filter_out is_def thms; 

249 
in 

250 
TRY (REPEAT_FIRST (resolve_tac (class_axms thy))) THEN 

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TRY (rewrite_goals_tac defs) THEN 

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TRY (REPEAT_FIRST (fn i => assume_tac i ORELSE resolve_tac non_defs i)) 

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end; 

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423  256 
(* provers *) 
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423  258 
fun prove term_of str_of thy sig_prop thms usr_tac = 
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let 
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val sign = sign_of thy; 
423  261 
val goal = cterm_of sign (term_of sig_prop); 
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val tac = axclass_tac thy thms THEN (if_none usr_tac all_tac); 

263 
in 

264 
prove_goalw_cterm [] goal (K [tac]) 

265 
end 

266 
handle ERROR => error ("The error(s) above occurred while trying to prove " 

267 
^ quote (str_of sig_prop)); 

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638  269 
val prove_subclass = 
423  270 
prove mk_classrel (fn (c1, c2) => c1 ^ " < " ^ c2); 
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423  272 
val prove_arity = 
2961  273 
prove mk_arity (fn (t, ss, c) => Sorts.str_of_arity (t, ss, [c])); 
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423  276 
(* make goals (for interactive use) *) 
277 

278 
fun mk_goal term_of thy sig_prop = 

279 
goalw_cterm [] (cterm_of (sign_of thy) (term_of sig_prop)); 

280 

281 
val goal_subclass = mk_goal mk_classrel; 

282 
val goal_arity = mk_goal mk_arity; 

283 

284 

285 

449  286 
(** add proved subclass relations and arities **) 
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3632  288 
fun add_inst_subclass c1_c2 axms thms usr_tac thy = 
289 
(writeln ("Proving class inclusion " ^ quote (Sorts.str_of_classrel c1_c2) ^ " ..."); 

423  290 
add_classrel_thms 
3632  291 
[prove_subclass thy c1_c2 (witnesses thy axms thms) usr_tac] thy); 
423  292 

449  293 
fun add_inst_arity (t, ss, cs) axms thms usr_tac thy = 
423  294 
let 
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val wthms = witnesses thy axms thms; 
423  296 
fun prove c = 
3632  297 
(writeln ("Proving type arity " ^ quote (Sorts.str_of_arity (t, ss, [c])) ^ " ..."); 
298 
prove_arity thy (t, ss, c) wthms usr_tac); 

423  299 
in 
300 
add_arity_thms (map prove cs) thy 

301 
end; 

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end; 